egg

everything is about the tensor product except the tensor product, which is about power

indeed!!

I wish I could have met Oded Schramm

3-strand braid Markov trace

5-strand braid Markov trace

another 5-strand braid Markov trace

15-strand braid Markov trace

Some links generated by taking the Markov trace of random words in the braid group 🧮

woah. a must-click

one of the things I've never liked about algebraic topology is how much one you seem to compute hard crunchy things (e.g. homology groups) by drawing loopy pictures. in probability it feels like you tend to understand what's visually going on with hard syntactic calculation, which I much prefer

reading this paper on the Poisson zoo and I love my field so much. I love thinking about lattice animals and random walks and factor of iid processes. I love probability, the tools, the language, the objects studied and how we study them

I love this, I also think of nilpotents as "thick" points

Uh huh

Wikipedia article called "Cabal (set theory)". The main text reads, The Cabal was, or perhaps is, a set of set theorists in Southern California, particularly at UCLA and Caltech, but also at UC Irvine. Organization and procedures range from informal to nonexistent, so it is difficult to say whether it still exists or exactly who has been a member, but it has included such notable figures as Donald A. Martin, Yiannis N. Moschovakis, John R. Steel, and Alexander S. Kechris. Others who have published in the proceedings of the Cabal seminar include Robert M. Solovay, W. Hugh Woodin, Matthew Foreman, and Steve Jackson. The work of the group is characterized by free use of large cardinal axioms, and research into the descriptive set theoretic behavior of sets of reals if such assumptions hold. Some of the philosophical views of the Cabal seminar were described in Maddy 1988a and Maddy 1988b.

👀

yeah seems like a wildly bad heuristic, especially when the "good at math" level here is pre-k math...

Summaring the problems in every maths department.

"semi-mature" is really pushing it

Okay this is embarrasing but I as a semi-mature probabilist only recently realized that the event {S_n = 0 infinitely often} is not in the tail sigma algebra (where S_n denotes a simple random walk, idk S_n = X_1 + ... + X_n for X_i iid centred e.g.). It is still in the exchangeable algebra though!

ME TOO it's so satisfying

This is a real sign from a real deli near the Wesleyan math department, and they put it up because the mathematicians were too engrossed in their mathematics discussions to efficiently order sandwiches. www.cbc.ca/radio/asitha...

I can't tell if I love or hate the terminology of going up and going down. On the one hand, extremely transparent name for a property. On the other hand, asking "Does this ring hom satisfy going up?" sounds mildly ungrammatical to me

image of Alexander Horned Sphere. made by Ryan Dahl, Creative Commons license

local lovecraftian horror the alexander horned sphere asking "please sir, I want some more". would you deny him?

I would rather whip cream by hand and give myself carpal tunnel (speaking from experience) than buy cool whip

I guess for us, the prototypical graphs are like Z^d, complete graphs on n vertices, or maybe a k-regular trees, perhaps the most boring graphs possible from a graph-theoretic perspective!

oh I very much feel this, as a probabilist I don't have the same conception of graphs that a finite graph theorist does at all, clearly. the most I would really think about is if a graph is bipartite. there's some intersection certainly, but I'm never thinking about like, Ramsey numbers

(he was thinking about d-dimensional hyperbolic space or something if I recall correctly and there's some relevant algebra there)

definitely feel this as a probabilist. was talking with one of the best percolation theorists in the world and he told me about a proud moment at a conference recently where he wrote down a short exact sequence for the first time. lol

i'm waiting for my poisson clock. i'm going to infect you at rate 1. you will not evade me

two years of having Stein's method explained to me and I still can't remember it

sensational energy here

give me an example! this is really interesting to me

it's crazy to me that I have a master's and I still am basically at strong undergrad level of good at math. like I was a strong undergrad and I feel like I never transcended it

it's actually insane to me how much good control we get over (some of these) models in this class, down to exact cumulative probability functions of the positions of multi-point particle systems at arbitrary times. and it comes from the richness of the algebra \lambda of symmetric functions etc.

out-of-left-field answer but Young tableaux and representation theory of S_n is one of the reasons why we have exact understanding of certain probabilistic models in the KPZ universality class, like e.g. TASEP. see arxiv.org/pdf/1212.3351